Kevin is 4 years older than William. Fifteen years ago, Kevin was 5 times as old as William. How old is William now?
Answer: We can use the given information to write down two equations that describe the ages of Kevin and William. Let Kevin's current age be $k$ and William's current age be $w$ The information in the first sentence can be expressed in the following equation: $k = w + 4$ Fifteen years ago, Kevin was $k - 15$ years old, and William was $w - 15$ years old. The information in the second sentence can be expressed in the following equation: $k - 15 = 5(w - 15)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $w$ , it might be easiest to use our first equation for $k$ and substitute it into our second equation. Our first equation is: $k = w + 4$ . Substituting this into our second equation, we get the equation: $(w + 4)$ $-$ $15 = 5(w - 15)$ which combines the information about $w$ from both of our original equations. Simplifying both sides of this equation, we get: $w - 11 = 5 w - 75$ Solving for $w$ , we get: $4 w = 64$ $w = 16$.